Download Built for Jumping: The Design of the

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Built for Jumping: The Design of the
Frog Muscular System
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sign (CAD) program. We determined muscle-tendon length changes by cutting either
the proximal or distal end of the muscle
(which was made inextensible by fixation
with formalin) and driving the hip or knee
joints, respectively, through their in vivo
three-dimensional angle changes [on the
basis of (II)] in a custom-made jig (12).
The SL excursion during the jump was
calculated from the SL value measured in
the crouched position and the percent
length change of the muscle determined
above. We determined the SL in the
crouched position by rapidly freezing resting
or active muscle at its in vivo muscle length
and measuring SL in frozen sections (13).
The SM is principally a hip extensor
muscle, with an average moment arm
around the hip of 4.4 mm and a flexor
moment about the knee of 0.08 mm. During six maximal jumps (distance = 0.67 +
0.03 m, mean SE), the SM shortened
7.51 0.17 mm (Fig. 1B) from an initial
length of 33.6 ±+ 0.35 mm. This corresponds to SL shortening from 2.34 pim (±+
0.013, n = 161, from four frogs) in the
crouched position to 1.82 ±+ 0.01 pim at the
point of takeoff (Fig. 2A) (14). Shortening
started 26 ±+ 3.4 ms after the start of the
EMG burst, and after an additional -5 ms,
the muscle attained a constant velocity of
0.10 muscle lengths per second
3.43
(ML/s; ML defined at 2.34 pIm; Fig. 1, A
and B). The constancy of muscle shortening velocity (md6/dt) reflects that during
jumping both the angular velocity of the
hip (dO/dt) and the moment around the hip
Gordon J. Lutz and Lawrence C. Rome*
Frogs must generate a high level of mechanical power when they jump. The muscular
system of frogs that jump is presumably designed to deliver these high powers. The length
changes and activation pattern that muscles undergo during jumping were measured, and
isolated muscle bundles were driven through this in vivo pattern. During jumping, muscles
generated maximum power. Specifically, the muscle fibers (i) operated at optimal sarcomere lengths, (ii) operated at optimal shortening velocities, and (iii) were maximally activated during power generation. Thus, many different parameters must have evolved in
concert to produce a system capable of this explosive jumping movement.
Over the past four decades much has been
learned about the mechanism of muscle
contraction (1, 2) and about the large
variation in the kinetics of contraction
(3). In contrast, we know little about how
muscle is used during locomotion. An
understanding of how muscle actually
functions in vivo may explain why contraction kinetics vary so greatly. We chose
to study the frog to explore muscle function during locomotion because most of
our understanding of the mechanism of
muscle contraction is based on frog muscle
(1, 2, 4). In addition, frogs recruit all of
their extensor muscle fibers during jumping (5), so isolated muscle experiments
can be related directly to muscle function
during locomotion. Finally, the jump of
the frog is a fundamentally different mode
of locomotion ("single shot" explosive
movement) than the cyclical movements
examined in fish (6) and scallops (7) and
thus provides the opportunity to examine
a muscular system evolving under different
,,
maximum power is generated, and (iii) be
maximally activated (9).
To test whether the muscular system is
designed to achieve these conditions, we
first measured the SL changes, V, and the
activation pattern of the semimembranosus
muscle (SM) during maximal jumps in the
frog, Rana pipiens. This was accomplished
by a combination of high-speed motion
pictures, anatomical analysis, and electromyography (Fig. 1).
Frogs were filmed from above and from
the side at 200 frames per second during
maximal jumps at 25°C. Electromyograms
(EMGs) were recorded with bipolar electrodes (6, 10) made of 50-pxm nickel wire
and were electronically synchronized to the
motion picture film to within ±0.5 ms (6).
The three-dimensional joint angle of the
hip and knee were determined from the
films by analysis with a computer-aided de-
±
±
±
(m) were nearly constant.
*To whom correspondence should be addressed.
Fig. 1. Frog muscle function during
A
Isolated muscle
Frog jumpC
jumping. (A) and (B) show the
or
3:
stimulation and length change pat81.oj i~ ~~~l
o.o
terns, respectively, that the SM un(3~~~~~~
E 2
dergoes during a maximal jump.
(C and D) An isolated muscle bun- W 1' 0o
die driven through the in vivo stimD
B Lag
o--0,0oo
ulation and length change patterns, and (E) the resulting force
2
2
production of the muscle. The isoEE
lated muscle bundles were stimulated at either 200 or 120 pulses
4
per second (pps), and there was
\
no significant effect of frequency
"
,
over this range. The stimulation duration was determined from the
8
EMG (29). The phase of the stimulus with respect to the length
Time(ms)E 100125
0.20.........
change was determined in the following manner. We determined the initiation of shortening by
0.12extrapolating the constant velocity portion of the length record back
to zero length (B). The lag was defined as the time between the
o...........o
onset of the EMG and the initiation of shortening. Because during
jumping the early portion of the length record was curved, digital
smoothing was used to obtain the correct shape of the computer-25
25 50 75 100125
Time (ms)
generated length change (D). The dashed line (E) is isometric force
and the dotted line is the steady-state force generated by the same
muscle at the same Vduring a force-velocity experiment (Fig. 2). The jump shown in (A) and (B) is
the longest measured (distance = 0.8 m, V= 3.78 ML/s), and this was reproduced in (C) to (E).
370
SCIENCE
constraints.
The jumping of the frog is one of the
most thoroughly studied locomotory movements (5, 8). During a maximal jump, a frog
accelerates from a stationary crouched position to high vertical and forward velocities in
under 100 ms (5, 8). To produce these rapid
increases in potential energy and kinetic energy, the muscles of the frog must generate a
high level of mechanical power. Ultimately,
the distance a frog travels is directly proportional to power production (5).
For the muscles of the frog to generate
their maximum mechanical power, they
must (i) operate over the plateau of the
sarcomere length (SL)-tension curve where
maximum force is generated, (ii) operate at
the appropriate V/Vmax (where V is shortening velocity during jumping and Vmax is
the maximum velocity of shortening) where
Department of Biology, University of Pennsylvania,
Philadelphia, PA 19104 and Marine Biological Laboratory, Woods Hole, MA 02543.
A
,,
l
'
-6
4
°-
-25
25
50 75
0.16
*
VOL. 263
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21 JANUARY 1994
Downloaded from www.sciencemag.org on March 16, 2008
·.i·zi
.::::.·1.·.:.5.:.·.::.I.:..:..·.:::::.::
To determine whether the SM generated maximum power during these in vivo
conditions, we used a computer-controlled
servo and stimulator system (6) to perform
isolated muscle mechanics experiments.
Several experiments, in which tension and
active SL (laser diffraction) were measured
during "fixed-end" tetani, showed that the
Fig. 2. Where does the SM
muscle operate on its SLtension and force-velocity
curves? (A) Results from
fixed-end tetani of two preparations (open and solid
symbols) show that the data
are well fit by the classic
SL-tension curve (2). The
SL-tension relation was not
studied at SL>2.35 p-m, because frogs do not use
these SLs during jumping
and because of well-known
experimental problems associated with fixed-end contractions at long SLs (2).
Muscle shortening during
jumping is shown by the arrow. (B) A typical force-velocity and power-velocity
standard frog SL-tension curve (2) fit the
SM data, so the standard curve was used to
represent the SL-tension curve of the SM
(Fig. 2A). During a jump, the SM operates
mostly over the plateau where maximum
force is generated (Fig. 2A). This suggests
that during evolution the muscle origin,
insertion, and angle of pennation have
A
1.0
0.8
//
0.6
0.4
0.2
02
Jumping
/
0.0
1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
Sarcomere length (gm)
300
200
250
o
150
200
power curve was
150
calculated from the force-15°i
velocity fit. At the V used
100
during jumping, the muscle
operates over the portion of
50
the power curve where at
least 99% of maximum pow0,o'
0
10
8
6
4
2
er is generated. Force is
Velocity (MI.s)
(Ms)
shown by open symbolsVelocit
and power is shown by closed symbols. At loads above 0.8 of isometric force (19), cubic splines
(dotted lines) were used to extrapolate the force-velocity curve to isometric force and the
power-velocity curve to zero power, respectively.
curve. The
y
In vivo
Step-ramp
Fig. 3. The SM muscle is maximally activated
C
A
for the entire shortening phase of jumping. To
e,
determine the time course of activation, we
o0compared the force generated by the muscle
shortening at the V of the fastest jump (3.78
1
ML/s) in contractions where the initial stimulus
with
amounts
various
by
preceded shortening
the steady-state force generated while shortenp
0.24
ing at the same V during the force-velocity
curve measurements (in which the muscle is-0.20
known to be maximally activated). (A and B)
The muscle underwent the in vivo length23
o.16 2
changes (A), with the first stimulus preceding
shortening by various times (shown by arrows,
0.12
times in milliseconds). (B) Force record of the
..
muscle given these lags; the dotted line is the
force level from the force-velocity curve. (C and
8
004.
D) The muscle undergoing the step-ramp protocol, with different lags. In this case, the step
imposed on the muscle was adjusted for the
0.0oo // 0.00~~~im
various lags so as to bring the force
down to the constant level associated with the V. In the case of 8 and 13 ms, no step was imposed,
as the force at the time of the step was below the force-velocity level. (C) Length change and (D)
force records of SM undergoing step-ramp protocol; dashed line in (B) and (D) is isometric force.
The dotted line in (D) represents force from the force-velocity curve. Each division on the x axes
represents 10 ms.
e^--
,
//
/
quicklyTim
SCIENCE
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VOL. 263
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21 JANUARY 1994
adjusted to give the appropriate gear
ratio [(change in body movement)/(change
in SL)] so that fibers shorten mainly over
been
the plateau during jumping. Although the
SM shortened somewhat beyond the plateau (15), it never produced less than 90%
of the force generation at optimal SL.
Isovelocity contractions (16) were used
to determine the force-velocity characteristics of the muscle. A force-velocity and
power-velocity curve from one preparation
are shown in Fig. 2B. Frog muscle at 25°C
can shorten faster and generate greater
power than muscles from most other animals (17, 18). On average (n 6), Vmax
was 10.35
0.20 ML/s (19) and maximum
7 W per kilogram of
power was 371
muscle mass. The V at which maximum
power was generated was 3.44 +± 0.13
ML/s, which matches closely the average V
during jumping (3.43 ML/s). This occurs at
a V/VN
0.33 (Fig. 2B). Although histochemistry (20) shows that the SM contains the two fastest twitch amphibian fibers
(amphibian type 1 and type 2), mechanics
experiments (18, 21) show relatively little
difference (-20%) in Vm,, between these
fiber types. This suggests that Vmx of each
fiber type has been adjusted during evolution such that during jumping, the muscle
operates at the appropriate V/Vma, for maximal power generation.
Although the SM shortens at the correct
SLs and V/Vma for maximum power generation, the question arises whether the muscle is stimulated for a sufficient time before
shortening to be maximally activated during jumping. For the jump of the frog, we
considered activation to be maximal if the
muscle generated the same force (and power) under in vivo conditions as it did at the
corresponding V during the force-velocity
experiments (where maximal activation
was achieved by stimulating the SM for 60
ms before shortening).
Force generation while the muscle underwent its in vivo length change and
stimulation pattern rose to about 60% of
isometric force and then fell to an average
constant level (41
2%), corresponding to
the V at which the muscle is shortening
(Fig. 1, C to E). Despite the short lag
between the EMG and muscle shortening
(18 ms), the force the muscle generated
under the in vivo conditions was greater
than or equal to the force generated at that
V on the force-velocity curve, suggesting
that the muscle was maximally activated.
For a more clear determination of the
time course of activation, the muscle was
driven through the in vivo length changes,
with the first stimulus preceding shortening
by different times (Fig. 3, A and B). When
the first stimulus preceded shortening by
less than 18 ms, the muscle generated less
force for much of the shortening phase of
=
±
±
=
±
371
Downloaded from www.sciencemag.org on March 16, 2008
o.~ 2I
eteevotea
g~~~~~g~~~~~i--...
~~~
(22),
activation processes
fast in both fiber types
are
sufficiently
to ensure
maximal
activation during jumping.
Comparison of isolated muscle and
whole animal power production further supports the conclusion that fibers were maximally activated and shows that most of the
extensor muscles in the frog hindlimb probably behaved similarly to the SM during
jumping. Peak power generated by the
whole frog during jumping was determined
from the films by measuring the change in
the position of the center of mass of seven
segments of the frog with time (23) and was
67.2 5.4 W per kilogram of body mass.
Because the maximum power generated by
the SM was 371 W per kilogram of muscle
mass and only about 17% of the body mass
(24) can be involved in powering jumping
[that is, maximum possible whole animal
power = 371 W/(kilogram of muscle) x
0.17 (kilogram of muscle/kilogram of body
mass) 63 W/(kilogram of body mass)], all
the muscle fibers from each extensor muscle
are probably recruited and stimulated at a
sufficiently high frequency (25) and shorten
over the appropriate SLs and V/Vmax for
maximum power generation during jumping. In addition, preliminary results for the
cruralis muscle, a large knee extensor, in±
=
dicate that it is activated and shortens
much like the SM (26).
Thus, the muscular system of frogs that
jump is designed so that the three necessary
conditions for maximum power generation
are met. In agreement with fish studies (27),
the values of a number of underlying parameters have evolved to meet the first two
conditions. Specifically, the fiber gear ratio
and myofilament lengths are set so that
muscles work mainly over the plateau of the
SL-tension curve, and the Vmax and the gear
372
ratio are set so that extensors operate at the
appropriate V/Vm, for maximum mechanical power generation. In addition, the present results show that during one-shot frog
jumps there is a third design goal met;
various processes involved in muscle activation [calcium release, binding to troponin,
crossbridge transitions (28)] are set to be
rapid enough to enable the muscle to be
maximally activated by the beginning of the
shortening phase of the jump. Finally, muscle force in the frog remains constant during
shortening, permitting maximum power to
be generated throughout a jump. By contrast, muscle force in animals using cyclical
movements, such as fish swimming, declines
during shortening (because of shortening
deactivation and early cessation of stimulation) so that the muscle can be subsequently
relengthened without resistance (6).
REFERENCES AND NOTES
Huxley and R. Niedergerke, Nature 173, 971
(1954); H. E. Huxley and J. Hanson, ibid., p. 973.
A. M. Gordon, A. F. Huxley, F. J. Julian, J. Physiol.
184, 170 (1966).
M. Barany, J. Gen. Physiol. 50, 197 (1967).
A. V. Hill, Proc. R. Soc. London Ser. B 126, 136
(1938); R. C. Woledge, N. A. Curtin, E. Homsher,
Energetic Aspects of Muscle Contraction (Academic Press, New York, 1985).
M. Hirano and L C. Rome, J. Exp. Biol. 108, 429
1. A. F.
2.
3.
4.
5.
(1984).
340 (1993).
R. L. Marsh, J. M. Olson, S. K. Guzik, Nature 357,
411 (1992).
L. R. Calow and R. M. Alexander, J. Zoo/. (London) 171, 293 (1973); J. M. Renaud and E.R. D.L.
Stevens, Cand. J. Zoo/. 61, 1284 (1983);
Lieber and C. G. Brown, Acta Anat. 145, 289
(1992).
From a molecular viewpoint, all of the crossbe engaged in active cycling and
bridges mustmust
be moving past one another at
the filaments
the appropriate speed for maximum power generation.
Frogs were anesthetized with MS-222 (1 mg/ml)
for the implantation procedure. The short electrodes were fed subcutaneously to a connecter
sutured to the frog's back.
R. M. Alexander, G. M. O. Maloiy, R. F. Ker, A. S.
Jayes, C. N. Warui, J. Zoo/. London 198, 293
(1982).
6. L. C. Rome, D. Swank, D. Corda, Science 261,
7.
8.
9.
10.
11.
12. The displacement of the cut end along the line of
action of the femur is equal to the muscle-tendon
joint (dL). The molength change about a given
ment (m) was calculated as the quotient of dL/de
where de is the joint angle change. The total
muscle-tendon length change was taken as the
sum of the dLs around the hip and knee. We
calculated the muscle length change assuming
the
length change in the connective tissue to be
negligible (14).
13. The in vivo length was set by killing the frog and
in the crouched posifastening the frog hindlimb
tion. The muscle was frozen by plunging the
hindlimb in liquid N2-cooled isopentane either
during stimulation of the motor nerve (active) or in
a relaxed state.
14. The total length change of the muscle-tendon
to occur in the muscle, on
complex was assumed
the basis of the following reasoning. The SL
measured in the active case was 2.21 ~m
(±0.014, n = 184, from three frogs) compared
with 2.34 i.m in the passive case, thus representdecrease in SL during maximum
ing an -5%
isometric tension. Because an -1.5% length
SCIENCE * VOL. 263 * 21 JANUARY 1994
15.
16.
17.
18.
19.
change is known to be associated with the intrinsic series elasticity of the fibers (16), the maximum that could be associated with the connective
tissue under isometric conditions is 3.5%. During
shortening, however, the muscle generated only
-40% of isometric force, setting an upper limit of
1.4% (that is, 40% x 3.5%) for the length change
associated with connective tissue during jumping.
This value seems reasonable because the SM has
only a short (-2 mm), stout tendon at the knee
and a direct attachment of the fibers at the pelvis.
This term was ignored because it has no effect on
Vand little effect on SL (0.03 ~m).
During jumps, force and power fell rapidly before
takeoff, so that very little power was generated at
the shorter SLs.
In this method, the muscle was given a highvelocity length step to unload the series elastic
component and thereafter shortened at constant
velocity [F. J. Julian, L. C. Rome, D. G. Stephenson, S. Striz, J. Physiol. 370, 181 (1986)].
J. M. Renaud and E. D. Stevens, J. Exp. Biol. 108,
57 (1984).
J. Lannergren, J. Muscle Res. Cell Motil. 8, 260
(1987).
Over the loads of 0.05 to 0.8 of isometric tension,
the force-velocity curves were well fit by the Hill
curve (Fig. 2B) when the curve was not constrained to pass through isometric tension. Typical r2 values for these curves were 0.99. At low
loads (0.01 to 0.03 of isometric tension), velocity
exceeded the Hill curve, and including these
points raised Vx by -5% as reported for single
frog fibers (16). These are the Vma values that
were reported here.
Downloaded from www.sciencemag.org on March 16, 2008
the jump, which signifies a lack of complete
activation. When the stimulus preceded
shortening by at least 18 ms (the shortest
lag measured during a jump), the force the
muscle generated was greater than or equal
to the corresponding force from the forcevelocity curve, suggesting the muscle was
maximally activated. Because the force early in the shortening phase was also effected
by the low V and a stretched series elastic
component, we drove the muscle through
the step-ramp protocol (16) [which rapidly
(-2 ms) unloads the series elastic component and attains the correct V; Fig. 3, C
and D] to determine how early in shortening the muscle becomes maximally activated. The activation time course was similar
to that in Fig. 3B, suggesting that the
smallest lag observed during jumping (18
ms) is sufficient for the fibers to be maximally activated throughout the shortening
phase. This also shows that although the
rate of activation processes may vary slightly in amphibian type 1 and type 2 fibers
20. R. S. Smith and W. K. Ovalle Jr., J. Anat. 116, 1
(1973).
Reggiani, S. Schiaffino, G. te
Kronnie, J. Physiol. 395, 679 (1988).
22. J. Lannergren, P. Lindblom, B. Johansson, Acta
Physiol. Scand. 114, 523 (1982).
23. This technique [M. A. Fedak, N. C. Heglund, C. R.
Taylor, J. Exp. Biol. 79, 23 (1982)] is inherently
noisy, so the peak values were obtained by averaging over 25 ms. This averaging may slightly
underestimate the actual maximal value, but a
21. K. A. P. Edman, C.
higher maximal value would only strengthen the
conclusion that the fibers are generating maximum
power during jumping.
24. The hindlimb extensors, hip abductors, and iliosacral muscles make up -17% of the frog's
mass.
comparison of muscle and whole animal
power generation shows that during jumping the
muscles were stimulated at sufficiently high freis
quencies to result in maximal activation. This
consistent with quantitative EMG analysis on the
SM that showed a spike frequency of 200 to 300
Hz.
26. G. J. Lutz and L. C. Rome, unpublished results.
27. L. C. Rome et al., Nature 355, 824 (1988); L. C.
Rome, R. P. Funke, R. M. Alexander, J. Exp. Biol.
154, 163 (1990); L. C. Rome and A. A. Sosnicki,
Am. J. Physiol. 260, C289 (1991).
28. M. A. Bagni, G. Cecchi, M. Schoenberg, Biophys.
J. 54, 1105 (1988).
29. Although the onset of the EMG was unambiguous,
the off-time was more difficult to determine precisely.
EMG consisted of a large-amplitude
Typically, the about
45 ± 3 ms that was followed by
signal lasting
a lower amplitude signal for an additional 23 ms.
Over the shortening phase of the contraction, the
forces were nearly identical in 45- and 68-ms duration stimulations. Specifically, the 45-ms stimulation
by the 68-ms
produced 96% of the work generated
stimulus, which was the maximum work of which the
muscle was capable. Hence, over the range of
possible EMG durations, the muscle is maximally
activated during the entire shortening phase.
30. We thank R. M. Alexander for useful discussions
and for suggesting the technique used to measure muscle length changes. Supported by
grants from NIH (AR38404) and NSF (IBN
25. The
9205397).
23 August 1993; accepted 28 October 1993